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#include "precomp.hpp"

// cvCorrectMatches function is Copyright (C) 2009, Jostein Austvik Jacobsen.
// cvTriangulatePoints function is derived from icvReconstructPointsFor3View, originally by Valery Mosyagin.

// HZ, R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge Univ. Press, 2003.



// This method is the same as icvReconstructPointsFor3View, with only a few numbers adjusted for two-view geometry
CV_IMPL void
cvTriangulatePoints(CvMat* projMatr1, CvMat* projMatr2, CvMat* projPoints1, CvMat* projPoints2, CvMat* points4D) {
    if (projMatr1 == 0 || projMatr2 == 0 ||
            projPoints1 == 0 || projPoints2 == 0 ||
            points4D == 0) {
        CV_Error(CV_StsNullPtr, "Some of parameters is a NULL pointer");
    }

    if (!CV_IS_MAT(projMatr1) || !CV_IS_MAT(projMatr2) ||
            !CV_IS_MAT(projPoints1) || !CV_IS_MAT(projPoints2) ||
            !CV_IS_MAT(points4D)) {
        CV_Error(CV_StsUnsupportedFormat, "Input parameters must be matrices");
    }

    int numPoints;
    numPoints = projPoints1->cols;

    if (numPoints < 1) {
        CV_Error(CV_StsOutOfRange, "Number of points must be more than zero");
    }

    if (projPoints2->cols != numPoints || points4D->cols != numPoints) {
        CV_Error(CV_StsUnmatchedSizes, "Number of points must be the same");
    }

    if (projPoints1->rows != 2 || projPoints2->rows != 2) {
        CV_Error(CV_StsUnmatchedSizes, "Number of proj points coordinates must be == 2");
    }

    if (points4D->rows != 4) {
        CV_Error(CV_StsUnmatchedSizes, "Number of world points coordinates must be == 4");
    }

    if (projMatr1->cols != 4 || projMatr1->rows != 3 ||
            projMatr2->cols != 4 || projMatr2->rows != 3) {
        CV_Error(CV_StsUnmatchedSizes, "Size of projection matrices must be 3x4");
    }

    CvMat matrA;
    double matrA_dat[24];
    matrA = cvMat(6, 4, CV_64F, matrA_dat);

    //CvMat matrU;
    CvMat matrW;
    CvMat matrV;
    //double matrU_dat[9*9];
    double matrW_dat[6 * 4];
    double matrV_dat[4 * 4];

    //matrU = cvMat(6,6,CV_64F,matrU_dat);
    matrW = cvMat(6, 4, CV_64F, matrW_dat);
    matrV = cvMat(4, 4, CV_64F, matrV_dat);

    CvMat* projPoints[2];
    CvMat* projMatrs[2];

    projPoints[0] = projPoints1;
    projPoints[1] = projPoints2;

    projMatrs[0] = projMatr1;
    projMatrs[1] = projMatr2;

    /* Solve system for each point */
    int i, j;
    for (i = 0; i < numPoints; i++) {   /* For each point */
        /* Fill matrix for current point */
        for (j = 0; j < 2; j++) {   /* For each view */
            double x, y;
            x = cvmGet(projPoints[j], 0, i);
            y = cvmGet(projPoints[j], 1, i);
            for (int k = 0; k < 4; k++) {
                cvmSet(&matrA, j * 3 + 0, k, x * cvmGet(projMatrs[j], 2, k) -     cvmGet(projMatrs[j], 0, k));
                cvmSet(&matrA, j * 3 + 1, k, y * cvmGet(projMatrs[j], 2, k) -     cvmGet(projMatrs[j], 1, k));
                cvmSet(&matrA, j * 3 + 2, k, x * cvmGet(projMatrs[j], 1, k) - y * cvmGet(projMatrs[j], 0, k));
            }
        }
        /* Solve system for current point */
        {
            cvSVD(&matrA, &matrW, 0, &matrV, CV_SVD_V_T);

            /* Copy computed point */
            cvmSet(points4D, 0, i, cvmGet(&matrV, 3, 0)); /* X */
            cvmSet(points4D, 1, i, cvmGet(&matrV, 3, 1)); /* Y */
            cvmSet(points4D, 2, i, cvmGet(&matrV, 3, 2)); /* Z */
            cvmSet(points4D, 3, i, cvmGet(&matrV, 3, 3)); /* W */
        }
    }

    /* Points was reconstructed. Try to reproject points */
    /* We can compute reprojection error if need */
    {
        int i;
        CvMat point3D;
        double point3D_dat[4];
        point3D = cvMat(4, 1, CV_64F, point3D_dat);

        CvMat point2D;
        double point2D_dat[3];
        point2D = cvMat(3, 1, CV_64F, point2D_dat);

        for (i = 0; i < numPoints; i++) {
            double W = cvmGet(points4D, 3, i);

            point3D_dat[0] = cvmGet(points4D, 0, i) / W;
            point3D_dat[1] = cvmGet(points4D, 1, i) / W;
            point3D_dat[2] = cvmGet(points4D, 2, i) / W;
            point3D_dat[3] = 1;

            /* !!! Project this point for each camera */
            for (int currCamera = 0; currCamera < 2; currCamera++) {
                cvMatMul(projMatrs[currCamera], &point3D, &point2D);

                float x, y;
                float xr, yr, wr;
                x = (float)cvmGet(projPoints[currCamera], 0, i);
                y = (float)cvmGet(projPoints[currCamera], 1, i);

                wr = (float)point2D_dat[2];
                xr = (float)(point2D_dat[0] / wr);
                yr = (float)(point2D_dat[1] / wr);

                float deltaX, deltaY;
                deltaX = (float)fabs(x - xr);
                deltaY = (float)fabs(y - yr);
            }
        }
    }
}


/*
 *	The Optimal Triangulation Method (see HZ for details)
 *		For each given point correspondence points1[i] <-> points2[i], and a fundamental matrix F,
 *		computes the corrected correspondences new_points1[i] <-> new_points2[i] that minimize the
 *		geometric error d(points1[i],new_points1[i])^2 + d(points2[i],new_points2[i])^2 (where d(a,b)
 *		is the geometric distance between points a and b) subject to the epipolar constraint
 *		new_points2' * F * new_points1 = 0.
 *
 *		F_			:	3x3 fundamental matrix
 *		points1_	:	2xN matrix containing the first set of points
 *		points2_	:	2xN matrix containing the second set of points
 *		new_points1	:	the optimized points1_. if this is NULL, the corrected points are placed back in points1_
 *		new_points2	:	the optimized points2_. if this is NULL, the corrected points are placed back in points2_
 */
CV_IMPL void
cvCorrectMatches(CvMat* F_, CvMat* points1_, CvMat* points2_, CvMat* new_points1, CvMat* new_points2) {
    cv::Ptr<CvMat> tmp33;
    cv::Ptr<CvMat> tmp31, tmp31_2;
    cv::Ptr<CvMat> T1i, T2i;
    cv::Ptr<CvMat> R1, R2;
    cv::Ptr<CvMat> TFT, TFTt, RTFTR;
    cv::Ptr<CvMat> U, S, V;
    cv::Ptr<CvMat> e1, e2;
    cv::Ptr<CvMat> polynomial;
    cv::Ptr<CvMat> result;
    cv::Ptr<CvMat> points1, points2;
    cv::Ptr<CvMat> F;

    if (!CV_IS_MAT(F_) || !CV_IS_MAT(points1_) || !CV_IS_MAT(points2_)) {
        CV_Error(CV_StsUnsupportedFormat, "Input parameters must be matrices");
    }
    if (!(F_->cols == 3 && F_->rows == 3)) {
        CV_Error(CV_StsUnmatchedSizes, "The fundamental matrix must be a 3x3 matrix");
    }
    if (!(((F_->type & CV_MAT_TYPE_MASK) >> 3) == 0)) {
        CV_Error(CV_StsUnsupportedFormat, "The fundamental matrix must be a single-channel matrix");
    }
    if (!(points1_->rows == 1 && points2_->rows == 1 && points1_->cols == points2_->cols)) {
        CV_Error(CV_StsUnmatchedSizes, "The point-matrices must have two rows, and an equal number of columns");
    }
    if (((points1_->type & CV_MAT_TYPE_MASK) >> 3) != 1) {
        CV_Error(CV_StsUnmatchedSizes, "The first set of points must contain two channels; one for x and one for y");
    }
    if (((points2_->type & CV_MAT_TYPE_MASK) >> 3) != 1) {
        CV_Error(CV_StsUnmatchedSizes, "The second set of points must contain two channels; one for x and one for y");
    }
    if (new_points1 != NULL) {
        CV_Assert(CV_IS_MAT(new_points1));
        if (new_points1->cols != points1_->cols || new_points1->rows != 1) {
            CV_Error(CV_StsUnmatchedSizes, "The first output matrix must have the same dimensions as the input matrices");
        }
        if (CV_MAT_CN(new_points1->type) != 2) {
            CV_Error(CV_StsUnsupportedFormat, "The first output matrix must have two channels; one for x and one for y");
        }
    }
    if (new_points2 != NULL) {
        CV_Assert(CV_IS_MAT(new_points2));
        if (new_points2->cols != points2_->cols || new_points2->rows != 1) {
            CV_Error(CV_StsUnmatchedSizes, "The second output matrix must have the same dimensions as the input matrices");
        }
        if (CV_MAT_CN(new_points2->type) != 2) {
            CV_Error(CV_StsUnsupportedFormat, "The second output matrix must have two channels; one for x and one for y");
        }
    }

    // Make sure F uses double precision
    F = cvCreateMat(3, 3, CV_64FC1);
    cvConvert(F_, F);

    // Make sure points1 uses double precision
    points1 = cvCreateMat(points1_->rows, points1_->cols, CV_64FC2);
    cvConvert(points1_, points1);

    // Make sure points2 uses double precision
    points2 = cvCreateMat(points2_->rows, points2_->cols, CV_64FC2);
    cvConvert(points2_, points2);

    tmp33 = cvCreateMat(3, 3, CV_64FC1);
    tmp31 = cvCreateMat(3, 1, CV_64FC1), tmp31_2 = cvCreateMat(3, 1, CV_64FC1);
    T1i = cvCreateMat(3, 3, CV_64FC1), T2i = cvCreateMat(3, 3, CV_64FC1);
    R1 = cvCreateMat(3, 3, CV_64FC1), R2 = cvCreateMat(3, 3, CV_64FC1);
    TFT = cvCreateMat(3, 3, CV_64FC1), TFTt = cvCreateMat(3, 3, CV_64FC1), RTFTR = cvCreateMat(3, 3, CV_64FC1);
    U = cvCreateMat(3, 3, CV_64FC1);
    S = cvCreateMat(3, 3, CV_64FC1);
    V = cvCreateMat(3, 3, CV_64FC1);
    e1 = cvCreateMat(3, 1, CV_64FC1), e2 = cvCreateMat(3, 1, CV_64FC1);

    double x1, y1, x2, y2;
    double scale;
    double f1, f2, a, b, c, d;
    polynomial = cvCreateMat(1, 7, CV_64FC1);
    result = cvCreateMat(1, 6, CV_64FC2);
    double t_min, s_val, t, s;
    for (int p = 0; p < points1->cols; ++p) {
        // Replace F by T2-t * F * T1-t
        x1 = points1->data.db[p * 2];
        y1 = points1->data.db[p * 2 + 1];
        x2 = points2->data.db[p * 2];
        y2 = points2->data.db[p * 2 + 1];

        cvSetZero(T1i);
        cvSetReal2D(T1i, 0, 0, 1);
        cvSetReal2D(T1i, 1, 1, 1);
        cvSetReal2D(T1i, 2, 2, 1);
        cvSetReal2D(T1i, 0, 2, x1);
        cvSetReal2D(T1i, 1, 2, y1);
        cvSetZero(T2i);
        cvSetReal2D(T2i, 0, 0, 1);
        cvSetReal2D(T2i, 1, 1, 1);
        cvSetReal2D(T2i, 2, 2, 1);
        cvSetReal2D(T2i, 0, 2, x2);
        cvSetReal2D(T2i, 1, 2, y2);
        cvGEMM(T2i, F, 1, 0, 0, tmp33, CV_GEMM_A_T);
        cvSetZero(TFT);
        cvGEMM(tmp33, T1i, 1, 0, 0, TFT);

        // Compute the right epipole e1 from F * e1 = 0
        cvSetZero(U);
        cvSetZero(S);
        cvSetZero(V);
        cvSVD(TFT, S, U, V);
        scale = sqrt(cvGetReal2D(V, 0, 2) * cvGetReal2D(V, 0, 2) + cvGetReal2D(V, 1, 2) * cvGetReal2D(V, 1, 2));
        cvSetReal2D(e1, 0, 0, cvGetReal2D(V, 0, 2) / scale);
        cvSetReal2D(e1, 1, 0, cvGetReal2D(V, 1, 2) / scale);
        cvSetReal2D(e1, 2, 0, cvGetReal2D(V, 2, 2) / scale);
        if (cvGetReal2D(e1, 2, 0) < 0) {
            cvSetReal2D(e1, 0, 0, -cvGetReal2D(e1, 0, 0));
            cvSetReal2D(e1, 1, 0, -cvGetReal2D(e1, 1, 0));
            cvSetReal2D(e1, 2, 0, -cvGetReal2D(e1, 2, 0));
        }

        // Compute the left epipole e2 from e2' * F = 0  =>  F' * e2 = 0
        cvSetZero(TFTt);
        cvTranspose(TFT, TFTt);
        cvSetZero(U);
        cvSetZero(S);
        cvSetZero(V);
        cvSVD(TFTt, S, U, V);
        cvSetZero(e2);
        scale = sqrt(cvGetReal2D(V, 0, 2) * cvGetReal2D(V, 0, 2) + cvGetReal2D(V, 1, 2) * cvGetReal2D(V, 1, 2));
        cvSetReal2D(e2, 0, 0, cvGetReal2D(V, 0, 2) / scale);
        cvSetReal2D(e2, 1, 0, cvGetReal2D(V, 1, 2) / scale);
        cvSetReal2D(e2, 2, 0, cvGetReal2D(V, 2, 2) / scale);
        if (cvGetReal2D(e2, 2, 0) < 0) {
            cvSetReal2D(e2, 0, 0, -cvGetReal2D(e2, 0, 0));
            cvSetReal2D(e2, 1, 0, -cvGetReal2D(e2, 1, 0));
            cvSetReal2D(e2, 2, 0, -cvGetReal2D(e2, 2, 0));
        }

        // Replace F by R2 * F * R1'
        cvSetZero(R1);
        cvSetReal2D(R1, 0, 0, cvGetReal2D(e1, 0, 0));
        cvSetReal2D(R1, 0, 1, cvGetReal2D(e1, 1, 0));
        cvSetReal2D(R1, 1, 0, -cvGetReal2D(e1, 1, 0));
        cvSetReal2D(R1, 1, 1, cvGetReal2D(e1, 0, 0));
        cvSetReal2D(R1, 2, 2, 1);
        cvSetZero(R2);
        cvSetReal2D(R2, 0, 0, cvGetReal2D(e2, 0, 0));
        cvSetReal2D(R2, 0, 1, cvGetReal2D(e2, 1, 0));
        cvSetReal2D(R2, 1, 0, -cvGetReal2D(e2, 1, 0));
        cvSetReal2D(R2, 1, 1, cvGetReal2D(e2, 0, 0));
        cvSetReal2D(R2, 2, 2, 1);
        cvGEMM(R2, TFT, 1, 0, 0, tmp33);
        cvGEMM(tmp33, R1, 1, 0, 0, RTFTR, CV_GEMM_B_T);

        // Set f1 = e1(3), f2 = e2(3), a = F22, b = F23, c = F32, d = F33
        f1 = cvGetReal2D(e1, 2, 0);
        f2 = cvGetReal2D(e2, 2, 0);
        a = cvGetReal2D(RTFTR, 1, 1);
        b = cvGetReal2D(RTFTR, 1, 2);
        c = cvGetReal2D(RTFTR, 2, 1);
        d = cvGetReal2D(RTFTR, 2, 2);

        // Form the polynomial g(t) = k6*t⁶ + k5*t⁵ + k4*t⁴ + k3*t³ + k2*t² + k1*t + k0
        // from f1, f2, a, b, c and d
        cvSetReal2D(polynomial, 0, 6, (+b * c * c * f1 * f1 * f1 * f1 * a - a * a * d * f1 * f1 * f1 * f1 * c));
        cvSetReal2D(polynomial, 0, 5, (+f2 * f2 * f2 * f2 * c * c * c * c + 2 * a * a * f2 * f2 * c * c - a * a * d * d * f1 * f1 * f1 * f1 + b * b * c * c * f1 * f1 * f1 * f1 + a * a * a * a));
        cvSetReal2D(polynomial, 0, 4, (+4 * a * a * a * b + 2 * b * c * c * f1 * f1 * a + 4 * f2 * f2 * f2 * f2 * c * c * c * d + 4 * a * b * f2 * f2 * c * c + 4 * a * a * f2 * f2 * c * d - 2 * a * a * d * f1 * f1 * c - a * d * d * f1 * f1 * f1 * f1 * b + b * b * c * f1 * f1 * f1 * f1 * d));
        cvSetReal2D(polynomial, 0, 3, (+6 * a * a * b * b + 6 * f2 * f2 * f2 * f2 * c * c * d * d + 2 * b * b * f2 * f2 * c * c + 2 * a * a * f2 * f2 * d * d - 2 * a * a * d * d * f1 * f1 + 2 * b * b * c * c * f1 * f1 + 8 * a * b * f2 * f2 * c * d));
        cvSetReal2D(polynomial, 0, 2, (+4 * a * b * b * b + 4 * b * b * f2 * f2 * c * d + 4 * f2 * f2 * f2 * f2 * c * d * d * d - a * a * d * c + b * c * c * a + 4 * a * b * f2 * f2 * d * d - 2 * a * d * d * f1 * f1 * b + 2 * b * b * c * f1 * f1 * d));
        cvSetReal2D(polynomial, 0, 1, (+f2 * f2 * f2 * f2 * d * d * d * d + b * b * b * b + 2 * b * b * f2 * f2 * d * d - a * a * d * d + b * b * c * c));
        cvSetReal2D(polynomial, 0, 0, (-a * d * d * b + b * b * c * d));

        // Solve g(t) for t to get 6 roots
        cvSetZero(result);
        cvSolvePoly(polynomial, result, 100, 20);

        // Evaluate the cost function s(t) at the real part of the 6 roots
        t_min = DBL_MAX;
        s_val = 1. / (f1 * f1) + (c * c) / (a * a + f2 * f2 * c * c);
        for (int ti = 0; ti < 6; ++ti) {
            t = result->data.db[2 * ti];
            s = (t * t) / (1 + f1 * f1 * t * t) + ((c * t + d) * (c * t + d)) / ((a * t + b) * (a * t + b) + f2 * f2 * (c * t + d) * (c * t + d));
            if (s < s_val) {
                s_val = s;
                t_min = t;
            }
        }

        // find the optimal x1 and y1 as the points on l1 and l2 closest to the origin
        tmp31->data.db[0] = t_min * t_min * f1;
        tmp31->data.db[1] = t_min;
        tmp31->data.db[2] = t_min * t_min * f1 * f1 + 1;
        tmp31->data.db[0] /= tmp31->data.db[2];
        tmp31->data.db[1] /= tmp31->data.db[2];
        tmp31->data.db[2] /= tmp31->data.db[2];
        cvGEMM(T1i, R1, 1, 0, 0, tmp33, CV_GEMM_B_T);
        cvGEMM(tmp33, tmp31, 1, 0, 0, tmp31_2);
        x1 = tmp31_2->data.db[0];
        y1 = tmp31_2->data.db[1];

        tmp31->data.db[0] = f2 * pow(c * t_min + d, 2);
        tmp31->data.db[1] = -(a * t_min + b) * (c * t_min + d);
        tmp31->data.db[2] = f2 * f2 * pow(c * t_min + d, 2) + pow(a * t_min + b, 2);
        tmp31->data.db[0] /= tmp31->data.db[2];
        tmp31->data.db[1] /= tmp31->data.db[2];
        tmp31->data.db[2] /= tmp31->data.db[2];
        cvGEMM(T2i, R2, 1, 0, 0, tmp33, CV_GEMM_B_T);
        cvGEMM(tmp33, tmp31, 1, 0, 0, tmp31_2);
        x2 = tmp31_2->data.db[0];
        y2 = tmp31_2->data.db[1];

        // Return the points in the matrix format that the user wants
        points1->data.db[p * 2] = x1;
        points1->data.db[p * 2 + 1] = y1;
        points2->data.db[p * 2] = x2;
        points2->data.db[p * 2 + 1] = y2;
    }

    if (new_points1) {
        cvConvert(points1, new_points1);
    }
    if (new_points2) {
        cvConvert(points2, new_points2);
    }
}
